Arithmetic board game

ABSTRACT

What is described is an arithmetic board game with a square grid board of spaces and a set of 135 playing tiles bearing indicia as pips representing fifteen each of the numerals zero through eight which are as well colored in nine distinct hues corresponding to the numerals. The challenge to players is to alternately form straight lines from their individually held six randomly drawn tiles as a row, column or diagonal line which interlocks with other lines previously placed on the playing board. Each of said lines is required to have a numerical sum of zero, nine or any multiple of nine. Scoring is based on the numerical summation of each newly formed line, one point earned for each nine value of said line. The numerical values of tiles are chosen to be represented in the form of pips, as on dominoes, in order to be equally readable from any viewing direction by two to four players and are as well keyed to colors of the tiles in order to be instantly recognizable at a glance of the playing board crucial to timely playing of the board game.

BACKGROUND AND SUMMARY OF THE INVENTION

The present invention is novel insofar as the specific objectives of play are not found in the prior art. The first objective of the present invention is to provide a new board game which will engage several players in arithmetic problem solving taking as its models such popular pastimes as Scrabble and Sudoku. Many games have been devised for two or more players to solve mazes in the manner of numerical versions of Scrabble or for solitary players to work out puzzlers such as the well known Sudoku but none have effectively combined the advantages of the two in a relaxed, socially entertaining version where, for example, such intriguing constructions as magic squares are at once accessible to the playing of a board game.

The second objective of the present invention is to provide a board game as described above where the physical embodiment of the game meaningfully contributes to the playing of the game. Often the prior art fails to recognize the importance color, for example, which in the present invention is an essential aspect to enable playing of the game.

The third objective of the present invention is to provide a board game as described above where, with just one given apparatus and set of rules of play, folks of various ages and skill levels in mathematics can interact creatively needing only the ability to add single digit numbers.

In furtherance of the above objectives an arithmetic board game is here described which is simple in design and is efficient in operation. Said game consists of a square playing board with a 15×15 grid of equal and contiguous squares, a set of 135 playing tiles comprised of nine subsets of 15 tiles, each of the subsets stamped with a particular number of pips, zero to eight in number, the subsets of tiles as well coated with nine distinct colors. Also provided is a cloth bag 6″ in diameter and 12″ in depth that contains all of the playing tiles hidden from view and a tile holding rack for use by each of the players.

Referring to FIG. 1, a plan view of the playing board of 15×15 like-sized squares is shown with a center square marked by X and twenty other squares marked as premium squares, total number of squares is 225;

FIG. 2 is a perspective view of one of the tile holding racks shown containing a random selection of six numerically stamped playing tiles;

FIG. 3 is a view of the playing board after a sample game has been played through. All of the lines that are rows or columns connecting two or more tiles and all of the lines that are diagonals connecting three or more tiles must sum to zero, nine or a multiple of nine. Of the 135 playing tiles in the game just two remain which cannot be played, which are viewed at the bottom edge of the board.

I will describe how the game is played in accordance with rules here stated utilizing the various elements set fourth by the present invention:

1. Each player draws a single tile from the bag, the highest value signifying the player who is designated to make the opening move, other players to follow clockwise. After tiles are returned to the bag and shuffled therein with the other tiles, each player blind-draws six tiles from the bag and sets them in his/her holding rack. Following each play, more tiles are drawn in order to maintain six tiles at all times throughout the game.

2. The first player is required to make a line of two to six tiles in any chosen order of the tiles extending in one direction as a contiguous row, column or diagonal covering the center square of the board with the requirement that the numerical sum of said line is zero, nine or a multiple of nine. Should this not be possible because no such sum can be made up from the given choice of tiles, then a single tile must be placed over the center square and a second tile set down diagonal to the first tile contiguous with it at any corner. One credit point is taken by the player for each increment of nine of the sum of the numerical values of the tiles in said line along with an extra point if playing all six tiles in the opening move.

3. The second player must form a line using one to six of his/her tiles incorporating at least one of the previously placed tiles, this line extending in any chosen direction as a row, column or diagonal. This line, including said incorporated tiles, must also sum to zero, nine or a multiple of nine and join lengthwise an existing line or intersect it. One credit point is taken for each increment of nine of the sum of the entire line thus formed (double if covering a premium square) and an extra point if playing all six tiles in the move. In addition, two-tile diagonal lines inadvertently formed when lines are intersected are credited if they have a sum of nine or not credited if they do not. Should the second player be unable to make the above move, he/she is required to place one tile diagonal to a tile already in place without placing it row or column-wise to any existing tile which placement would necessarily result in forming a row or column of two tiles whose sum is not nine; all rows and columns must have a sum of zero, nine or a multiple of nine regardless of their lengths.

4. Subsequent plays must similarly form a single line of tiles that incorporates one or more tiles previously placed. The line that is thus formed plus any additional line(s) that might result from connection(s) with other tiles previously placed on the board must each have sums of zero, nine or a multiple of nine. All such lines are credited in the usual way plus double credit for premium squares that are covered (triple credit if covering two premium squares in a single move) and one credit point for the use of all six tiles in a single play; in every case, rows or columns formed of two or more tiles and diagonals formed of three or more tiles must each sum to zero, nine or a multiple of nine.

5. Play ends and credit points are tallied, deducted by one point for each nonplayed tile when a player places all of his/her remaining tiles in a single move and no tiles remain to be drawn or when any player finds upon inspection that no legal move is further possible.

6. A simplified game is easily adapted from the version described in 1.-5. above by eliminating the rule that specifies diagonal lines of play. For this version, players form only rows and columns of their tiles, disregarding all diagonal lines that may be co-formed. This easier game can usually be played through in less than half the time and is well suited as an introductory game for beginners.

While a preferred embodiment is fully described herein, it is understood that various modifications may be made as may fall within the scope of the invention. 

What I claim as new and desire to secure by Letters Patent of the United States is:
 1. A numerical problem game for two to four players, equally and readily legible from any of four viewing directions by said players, comprising: a playing board subdivided by lines marked thereon into a grid of like and contiguous playing squares; a playing set of square tiles numbering about 60% as many as the number of said playing squares, each of the said tiles of the same surface area as said playing squares; a tile holding rack which each player must fill with six of said tiles prior to making his/her play, said rack designed to display six tiles at a convenient angle for view by a player yet concealed from view by other players; a cloth receiving bag for containing said playing set of tiles, said bag passed from player to player on the occasion of each play in order that each player may take in blind-draw his/her compliment of six of said playing tiles each; and a box sized to store all of the game parts.
 2. A numerical problem game of claim 1 having a playing board comprising: cloth material that may lay flat on any level table, said material of a flexible nature that can be rolled into a cylindrical form for storage in said box, said cloth coated with clear silicone rubber for added frictional purchase with said playing tiles to help prevent worrisome slipping of said tiles during play; and printed lines which subdivide the playing area of said board into like-sized playing squares with an X marking the board's center square to indicate the position for an opening play by a first player of the game, and further markings in a plurality of certain other of said squares to indicate premium squares.
 3. A numerical problem game of claim 1 having a playing set of square tiles comprising: individual said tiles made of wood or plastic of a thickness which allows a player to stand said tile on its edge in a tentative location on a playing square of said board to be viewed and studied by a player before finalizing his/her play by laying said tile into said square; pips stamped into top, square surfaces of said tiles, said pips numbering zero to eight that indicate nine different numerical values ranging from zero to eight, respectively, the number of said pips being equally and readily legible from any viewing direction by all players; colors painted onto top, square surfaces of said tiles, said colors being nine distinct hues associated with each of the nine said numerical values, said colors lending facility for quickly identifying locations of any given numerical value of said tiles on said board at a glance by a player during his/her decision making process; and a plurality of such as number about 60% of the number of playing squares of said board so that a game may be played to its conclusion, viz., placement of all or most of said playing set of tiles on said board in accordance with the rules of the game.
 4. A numerical problem game of claim 1 having a cloth receiving bag constructed so that: the said playing set of tiles is amply contained with some slack space so that said tiles can be readily shuffled within said bag, and so that sufficient depth is provided by said bag to allow a player to reach with one hand and wrist into said bag to grasp a desired number of said tiles without seeing numeric values of same before draw of said tiles from said bag; and an external tying chord is attached to said bag that can be threaded around the outside of said bag and tied to secure the said tile set within said bag for storage in said box. 